Languages:

Related Data and Programs:

BALL_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit ball in 3D.

CIRCLE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the surface of the unit circle in 2D.

CUBE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit cube in 3D.

DISK_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit disk in 2D.

HYPERBALL_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit hyperball in M dimensions.

HYPERCUBE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit hypercube in M dimensions.

HYPERSPHERE_MONTE_CARLO,
a C++ library which
uses the Monte Carlo method to estimate the integral of a function
over the surface of the unit hypersphere in M dimensions.

HYPERSPHERE_PROPERTIES,
a C++ library which
carries out various operations for an M-dimensional hypersphere, including
converting between Cartesian and spherical coordinates,
stereographic projection, sampling the surface of the sphere, and
computing the surface area and volume.

LINE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the length of the unit line in 1D.

POLYGON_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of a polygon in 2D.

PYRAMID_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit pyramid in 3D.

SIMPLEX_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit simplex in M dimensions.

SPHERE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the surface of the unit sphere in 3D.

SQUARE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit square in 2D.

TETRAHEDRON_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit tetrahedron in 3D.

TRIANGLE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit triangle in 2D.

WEDGE_INTEGRALS,
a C++ library which
returns the exact value of the integral of any monomial
over the interior of the unit wedge in 3D.

Reference:

Gerald Folland,
How to Integrate a Polynomial Over a Sphere,
American Mathematical Monthly,
Volume 108, Number 5, May 2001, pages 446-448.